Monday, September 24, 2012

An Efficient Frontier for Retirement Income

I’ve finished a new research paper called, “An Efficient Frontier for Retirement Income.” 

First, the punchline: with a 4% withdrawal rate to meet lifestyle spending goals, a 65-year old heterosexual couple is best served by combinations of stocks and fixed single-premium immediate annuities (SPIAs). At current product pricing levels, there is little need for bonds, inflation-adjusted SPIAs, or immediate variable annuities with guaranteed living benefit riders (VA/GLWBs).

This paper provides a framework for retirees to choose how to allocate their retirement assets between stocks, bonds, inflation-adjusted SPIAs, fixed SPIAs, and VA/GLWBs.

The basic idea is not original to me. As I often say: Moshe Milevsky already did it. In this case, he developed the ideas of product allocation and the efficient frontier for retirement income. But I think I’ve made some useful enhancements and improvements to his underlying framework.

As I’ve been thinking about financial goals for retirement, I think they can be boiled down to two objectives. It’s not just a matter of avoiding financial wealth depletion as is assumed in safe withdrawal rate studies. Rather, the two competing objectives are (1) to support minimum spending needs and lifestyle spending goals as best as possible, and (2) to maintain a buffer of financial assets either for a legacy or to use as a reserve for managing risks, such as expensive health shocks, divorce, unexpected needs of other family members, severe economic downturns, or other types of emergency needs. Generally, there is a tradeoff between these objectives, and retirees need to determine how much they value each objective and where they find the appropriate balance between them.

This research will help with the decision by plotting how 1,001 different product allocations perform with respect to meeting the two objectives, and then identifying the efficient frontier of product allocations. This efficient frontier tells you the allocations which support the highest reserves of financial assets for a given percentage of spending needs which can be satisfied, or, alternatively, the highest percentage of spending needs which can be satisfied for a given reserve of remaining financial assets. Any of the product allocations on the efficient frontier represent a potentially optimal point, and retirees can then choose which one they think best balances their own objectives.

The basic case study I use is a 65-year old couple who has an inflation-adjusted lifestyle spending goal of 6% of retirement date assets. Following the arguments made by noted financial planners such as Michael Kitces, Jonathan Guyton, and Harold Evensky, I also assume that this couple will be quite sad if they can’t meet their lifestyle goal, and so I assume their minimum spending needs are also 6%. They have a Social Security benefit equal to 2% of their retirement date assets, and so to meet their lifestyle goal, they need to generate additional income equal to 4% of their retirement date assets.

The following figure shows how their 1,001 product allocation possibilities perform. I’ve highlighted in blue all of the allocations which only consist of stocks and bonds without any annuitization. These outcomes reflect some of the worst possible results for meeting spending needs. Also, I’ve highlighted most of the efficient frontier with a red curve. These are the allocations between only stocks and fixed SPIAs.  

With the characteristics of this case study, what I find supports my earlier intuition that optimal retirement income strategies consist of partial annuitization with SPIAs. More strongly, it consists of mixing stocks with fixed SPIAs. I was surprised that fixed SPIAs perform better than inflation-adjusted SPIAs, but Joseph Tomlinson explains that this is because inflation-adjusted SPIAs are relatively overpriced. Also, interestingly, there is no need for retirees to hold bonds. SPIAs are like super bonds with no maturity dates and which boost retiree returns with mortality credits. Also, confirming my earlier intuition, GLWBs don’t really help and retirees can find some combination of stocks and fixed SPIAs which will better support both financial objectives than any allocation that includes a portion devoted to GLWBs. Again, these results are specific to the case study in question. Changing lifestyle goals, minimum spending needs, age and marital status of the retirees could all change which product allocations are on the efficient frontier.

Improvements I’ve tried to make to existing studies include basing both the annuity prices and the market return assumptions on current market conditions so as to avoid biasing the results against annuities, using low cost versions of each strategy as are available from companies like Vanguard, and discussing results in terms of different percentiles from the distribution of outcomes, rather than just the mean or median. Also, I think the way I’ve defined the percentage of lifetime spending needs which are satisfied is a step forward to more properly define the magnitude of success and failure. It is broader, as it can deal with both inflation-adjusted and fixed guaranteed income sources, and also it can better account for what happens with strategies using variable spending patterns.

If you are interesting in the process of building retirement income strategies, please have a look at this new article.


  1. Wade
    Great article and I love your paper.
    Getting the right splits in the product allocation is something we are spending some time considering here.
    The dominance of the partial annuity strategies in your chart is consistent with out work here, but I suspect many will find the level of dominance a little surprising.
    One question I have is in regard to the nominal/ indexed annuity differences. I understand why the nominal is on the frontier, given pricing and the effective discount rates. However, how far away is the indexed frontier in your model, and indeed the VA frontier. I would be very interested to see your figure with the 4 frontiers of stocks with bonds/ fixed SPIA/ nominal SPIA/ VA as a comparison.

    1. Aaron, thanks.

      I just made a new post which includes this figure.

  2. Hi Wade. As the resident liability driven investing (LDI) guy, I'd argue that the SPIA is a proxy for a long series of individual bonds timed to match the client's income needs. LDI portfolios often underlie the annuity pool.

    I agree that a total return approach to bonds does not serve a particularly useful role in a retirement income portfolio; especially in a rising rate environment because total return lags individual bonds held to maturity (turnover in a bond fund causes losses to be realized whereas the individual bonds receive their original YTM). Systematic withdrawal from a bond fund exposes the investor to all sorts of risks that negatively impact retirement income including interest rate risk and sequence risk.

    Building a dedicated bond portfolio, however, is essentially uncoupling the annuity portfolio from the insurance product. Dedicated Portfolio Theory outlines a version of LDI where individual bonds are timed specifically match a client’s income needs. The objective function is to minimize the cost using the given inventory of bonds. What that means is that an advisor can solve for a client’s specific cash flow needs, including lumps (for expenditures like major purchases and vacations), assumed inflation and RMD for the least cost.

    The day you build a dedicated portfolio for a client, you know its worst case scenario, which is the YTM on the underlying bonds (which is positive). Build it with CDs and Agency bonds and I will argue that the creditworthiness of the issuers is far stronger than the guarantee of an insurance company (AIG for example).

    One advantage that the insurance company should have going for them is mortality credits, but unfortunately for clients, insurance companies seem to price their product so that they keep the value. So when you compare a dedicated approach to an annuity, the dedicated portfolio tends to be the cheaper solution.

    Combine a dedicated income portfolio with an approach like Branning’s Modern Retirement Theory and you have a powerful way to match the portfolio cash flows to specific cash flow needs. It becomes very intuitive to the client and very flexible if you use a goals based benchmark, like our Critical Path, to drive decision making about funding the layers of goals.


    1. Brent, thanks. I'm looking forward to talking with you about this more on the phone.

    2. "Turnover in a bond fund causes losses to be realized whereas the individual bonds receive their original YTM. Systematic withdrawal from a bond fund exposes the investor to all sorts of risks that negatively impact retirement income including interest rate risk and sequence risk."

      --Any research out there to back this up? It seems this has become an axiom of sorts among advisors. I believe mathematically (ignoring transactions costs) a bond fund with reinvested dividends and held to duration will provide the same return as holding an individual bond to duration. The implication that bond funds are subject to interest rate risk and individual bonds are not is flat wrong. Wade, any research out there that compares a bond fund to individual bonds? Obviously for specific liability matching bond makes sense, but for general spending needs which 90% of a retirement portfolio is used for I do not buy that individual bonds are better than a fund which are more cost effective and liquid (assuming you are interested in more than just treasury bonds)

    3. Eric,

      You are using the phrase "held to duration." Do you mean "held to maturity"? It's not the same thing, but it seems that this is what you mean. Though, of course, you can't hold a bond fund to maturity. But you could hold it to duration. But to eliminate interest rate risk from an individual bond, you have to hold to maturity rather than to duration.

      You've also got to distinguish between holding a lump-sum investment in a bond fund without any new investments or withdrawals. Then your argument might be more applicable, though I don't know of specific research about it. It seems the answer would depend on whether all of the bonds held in the fund are held to maturity, and also there is an issue of reinvestment risk within the bond fund as bonds matured before the date that the fund owner wants to spend the money.

      When you are withdrawing from a bond fund though, interest rate risk and sequence risk always becomes relevant. I think Brent's statement is correct.

  3. Thanks for this article. It's heavy lifting for the average reader. I hope you will further consider converting the article into something slightly less esoteric so that a non-academic reader can more easily grasp the concepts discussed. Thank you.

    1. Thank you.

      That is essentially what I was trying to do with the blog post version. As I'm thinking about this stuff all the time, I may be losing track of which parts are clear and which parts are not clear. If you could provide some guidance about what, in particular, you find confusing, I would appreciate it.

    2. Mike Piper, one of the leading financial writers whose specialty is explaining things very well and very succinctly and clearly, has taken a stab at writing about this topic. I hope it helps:

      Oblivious Investor, Retirees: Should You Get Rid of Your Bonds?

  4. How about a little calculator that I can put my numbers in and see what I get? That would help us newbie DIY's.

    1. Ultimately, that could be where all of this is heading. But I'm not there yet. I don't know how to make interactive versions for the Internet. Sorry. But yes, some software is needed so that people can input their specific cases.

    2. That would be great. Being only 55 it would be interesting to see what the best portfolio would be. I've read the sweet spot for SPIA's is nearer to 70 so it may be I would need to switch/adjust as I get closer to that age.

    3. Yes, delaying annuitization will probably improve the efficient frontier. I still need to get to that.

  5. I'm not sure how complicated the calculator(s) would need to be, but I've written some relatively simple ones in Javascript. Send me an email if you want to see the page they are on.

    Plus, there are numerous programmers out there that I'm sure could do what you need and probably not be too expensive. Find one that can create a Mobile App and you potentially have a money maker (FYI: I am not an app designer). :O)

    As to the graph, it seems that neither method satisfies 100% of the lifetime spending need, is that correct? It seems the best you can hope for is about 98%. Of course that leaves about 30%-40% to cover unexpected expenses or leave to the heirs. Would that actually mean you would most likely make it? To what age is it assumed they live to?

    1. Chris,

      My understanding is that the x-axis shows the 10th percentile outcome for each allocation. In other words, for each allocation, 90% of the outcomes are better than the corresponding point plotted on the graph. That's how there's still an ending value greater than $0 most of the time.

    2. Chris,

      Thanks for the info about making a calculator. I will look into that more once I get all the features added which I think are needed first.

      Mike is right. The y-axis just gives you an idea about how much you can expect to have left on average (50% of the time there will be more, and 50% of the time there will be less), whereas the x-axis shows how much you can spend in a bad luck scenario.

      These are not the same points in the distribution, and I think this is a confusing point that would be nice to improve somehow. It's not the case that the leftover assets from the y-axis can be used to fill in the needs on the x-axis, because in some of the simulations you do run out of financial assets. That is the point that the x-axis is trying to get at.

      About your other question, the survival probabilities go through age 119, though the probability of living that long is extremely low. But it is possible.

  6. Wade, thanks for the continuing, excellent new research. Especially appreciate that you are building on others' work (Milevsky, and Otar has done similar).

    Very interesting to look at annuities as "super bonds," then leave bonds out of the investment portfolio altogether. But that leaves a question: how can we consider 100% stocks as a buffer/emergency reserve? They don't really satisfy that objective, due to volatility.

    Thanks again.


    1. Darrow, thanks. I still need to read Otar. That is a gaping hole in my background. I have his 2 books. I didn't realize that he has done something similar. I will check that.

      You ask a good question. I am not thinking of a reserve fund in the traditional sense here, in that you have 6 months or whatever of spending needs set aside in less volatile assets. Actually, you should still probably have that, but it is not incorporated here.

      That reserve of assets I am thinking of is more broad and goes beyond your lifestyle spending goals. There are many potentially very expensive risks, and one clear way to manage those risks with with a buffer of financial assets. And that y-axis is sort of a before-the-fact expectation about the amount of assets you can hope for on average. I think for many people it will be less important than meeting spending needs, which is why I represent it just as the median outcome instead of one of the worst-case outcomes. But I should explore some more about different definitions for the y-axis. 100% stocks definitely has a bigger up-and-down distribution than the other possibilities, that is for sure.

  7. Great article.

    Im curious though, what would the results have been taking overall taxes into consideration say by using tax free muni bonds.

    I would think the overall tax situation may alter things but im not really sure.

    1. Thanks, taxes is a complicated issue and I am not sure if there is any general answer as each person will have a different case.

      Annuities have some tax deferral properties, but then all of their income is taxed at regular income tax rates.

      Systematic withdrawals have more taxes upfront when the portfolio is larger and interest and dividends accrue, but also there is some beneficial tax treatment for dividends and capital gains.

      Taxes are certainly important, but I think each person will have a different set of circumstances that they will need to incorporate before making a final decision.

  8. Wade, I saw this link on Oblivious Investor. As I mentioned in the comment section there, I believe it's the pooling of longevity risk that makes annuities superior to bonds. However, I question the role of fees... Perhaps this is a basis for further study? Also, what's the sensitivity to lifestyle choices and deviation from assumptions? That is to say, on a practical level, how does life dependency affect the conclusions in this study?

    1. Thanks. Yes, I think you are right. Fees are surely important. But I am using real SPIA quotes, which have the implicit fees already incorproated. All of the strategies I consider are based on the prices for customers at Vanguard.

      About lifestyle choices, are you referring to what I call the lifestyle goal? I did make a more recent blog post which also shows the results for a 1%, 3%, and 5% withdrawal rate to achieve the lifestyle goal.

  9. I like your new paper assessing Stocks & SPIAs. I decided to follow a stock/SPIA ladder strategy after much reading, doing some of my own analysis, and researching bonds and bond funds. SPIAs do not get enough attention and I hope this will get the industry rolling. It seems to me that we have two different industries that don't have much interaction: Insurance companies and stock/bond brokers, each wanting to sell their own package. My simple analysis showed that there's a good chance you can leave a decent inheritance using stocks/SPIAs. Also, having longevity insurance with SPIAs avoids some major problems with bonds and bond funds: difficulty in selection, interest and default risk, bond ladders aren't liquid (you can't just easily change their size),... SPIAs help with two other thing that don't get much attention when you reach your mid-80's: (1) will you have the mental acuity to assess you financial situation, and (2) how emotionally difficult will it be to withdraw huge % from your nest egg as predicted by the 4% model. I hope to see more on this topic.

    1. Thank you for sharing. This is a great summary of a whole lot of important and relevant issues! You are right about cognitive issues, and also that is a good point about how people don't realize that 4% is designed specifically for a 30 year retirement and the withdrawal rate can be higher for shorter retirement durations.

  10. "Heterosexual" couple??? Is that really important? Your homophobia is showing,Wade.

    1. I hope you are joking.

      I am trying to specifically be inclusive rather than homophobic, actually, by not automatically assuming that the default type for a couple is opposite sex.

      Yes, it is important. Because mortality rates and survival probabilities differ for men and women, so a same-sex couple would have a different outcome than an opposite sex couple.

  11. Thank you so much, Dr Pfau, this is really helpful research.
    For some, living on the "frontier" of SPIAs and stocks is obviously the place to be.
    My questions concern whether living right on the frontier is the best place for most retirees.
    Given all the things that could go financially wrong over 30 years of retirement, most retirees would want, (in early retirement at least)to retain a significant percentage of liquid assets.
    My guess is that most would be prudent to perhaps start with annuitizing only what is needed (along with soc. sec) to provide survival spending: food, housing, health). Then over the years they could do gradual annuitizing to take advantage of the "frontier" (and of increasing SPIA returns as one ages)
    The problem comes for those who annuitize only a small amount of assets at first (eg 25% ) and put ALL the rest in stocks. If the stock market does really bad for several years (especially early in retirement) withdrawals for emergencies and other basic non-survival spending (eg a vehicle) could devastate those funds.
    Surely it would be better in the early years of retirement to have a small amount of cash and bonds to avoid touching those stocks for say 4-5 years.
    perhaps an allocation % might look something like this

    age SPIAs cash bonds stocks
    65 25 10 15 50
    70 35 10 10 45
    75 50 10 5 35
    80 65 10 5 20
    85+ 80 10 0 10

    while such an approach gets most of the benefits of the "frontier", by staying back a little from the front it reduces the chances of getting shot by nasty arrows of drastic stock downturns.
    The headline from your research ,then, is maybe not "maybe you dont need bonds in retirement" but rather "you should consider converting most of your bonds into annuities".
    I appreciate your research is theoretical at this stage and cannot answer these issues completely, but I look forward to the practical applications that I am sure will eventually come.
    I look forward in eager anticipation.


  12. sorry for the allocation formatting. I will try something different, see if it comes out any better


  13. Derek,

    Thank you. Your suggestion to convert bonds into annuities could very well be right. What you are saying sounds quite reasonable and I hope to be able to simulate those types of scenarios as well one of these days.

    Thank you, Wade

  14. 4/8/13. I just read your Efficient Frontier for Retirement Income. I am interested in a SPIA. I believe the monthly annuity you will receive is very dependent on the current interest that you can currently get on common investments. Since we are currently in a ridiculous time of extremely low rates. Wouldn't it be a bad time to start a SPIA. That is, What are the trade-offs of waiting for the interest rates to go up.
    I am only anonymmousw because I am not familiar with blogs.

  15. Hi, Wade, A very interesting article, with lots to think about. Would it be correct to assume that a joint lifetime pension benefit would fit into "the equation" just as well as an SPIA? Thanks for your efforts to educate.


    1. Hi, thank you, and yes. Though you might like to add that separately at the start in the way that Social Security is added separately. It will then suggest less need for SPIAs than without the pension.

  16. Great article. Thank you for speaking at our income planning summit in Indianapolis a couple of weeks ago. It was great to have our unique income strategies validated with your research. Based on your later research you co-authored for Morningstar where the new safe rate is 2.8%...would you make any changes to the efficient frontier work as it relates to having more SPIAs?

    1. Thanks Steve.

      It was a pleasure speaking. About the efficient frontier, the thing is that all the stock/SPIA combos are on the frontier. No SPIAs to 100% SPIAs. The point one chooses depends on personal preferences, which in turn depend on capital market expectations. It's hard to say for sure what direction most people would lean with this consideration, but at least the payout rate on a SPIA looks more attractive as one becomes increasingly pessimistic about a sustainable withdrawal rate.

  17. The 4% rule is deceptive. From Jan 1 1999 to Jan 1 2014 a portfolio of 33% S&P stocks and 67% aggregate bond market index provided a return on 5.6% when a simple elementary annual re-balancing strategy was employed. Best of all the bond/stock portfolio is 100% liquid, taxed at a lower rate, and you WILL get a better return on investment when it's all said and done. With annuities they bait you with the high interest payment rate but screw you with the ROI.

    1. Thank you, but I think there may be some factual problems with what you are saying. Just quickly about the final point, I hope people are not confused about the difference between an annuity payout rate and the underlying internal rate of return. I never found that point to be confusing, and thus never viewed any sort of bait and switch there. I can't remember hearing anyone state that incorrectly before either.